论文标题
基于Choquet的模糊粗糙集
Choquet-Based Fuzzy Rough Sets
论文作者
论文摘要
当对象之间存在不明智的概念时，模糊粗糙集理论可以用作处理不一致的数据的工具。它通过提供概念的下层和上近似来做到这一点。在经典的模糊粗糙集中，分别使用最小和最大运算符确定下部和上部近似值。这对于机器学习应用是不可取的，因为它使这些近似值对外围样品敏感。为了减轻此问题，引入了有序加权平均（OWA）的模糊粗糙集。在本文中，我们展示了如何通过模糊的量化来直观地解释基于OWA的方法，然后将其推广到基于Choquet的模糊粗糙集（CFRS）。该概括具有理想的理论特性，例如二元性和单调性。此外，它为机器学习应用提供了更大的灵活性。特别是，我们表明它可以实现离群检测算法的无缝集成，以增强基于模糊粗糙集的机器学习算法的稳健性。
Fuzzy rough set theory can be used as a tool for dealing with inconsistent data when there is a gradual notion of indiscernibility between objects. It does this by providing lower and upper approximations of concepts. In classical fuzzy rough sets, the lower and upper approximations are determined using the minimum and maximum operators, respectively. This is undesirable for machine learning applications, since it makes these approximations sensitive to outlying samples. To mitigate this problem, ordered weighted average (OWA) based fuzzy rough sets were introduced. In this paper, we show how the OWA-based approach can be interpreted intuitively in terms of vague quantification, and then generalize it to Choquet-based fuzzy rough sets (CFRS). This generalization maintains desirable theoretical properties, such as duality and monotonicity. Furthermore, it provides more flexibility for machine learning applications. In particular, we show that it enables the seamless integration of outlier detection algorithms, to enhance the robustness of machine learning algorithms based on fuzzy rough sets.
